Theorems · Theorem · order theory
Order.Ideal.isPrime_of_mem_or_compl_mem
∀ {P : Type u_1} [inst : BooleanAlgebra P] {I : Order.Ideal P} [I.IsProper], (∀ {x : P}, x ∈ I ∨ xᶜ ∈ I) → I.IsPrime- Defined in
- Mathlib.Order.PrimeIdeal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Compl.complstatement and proof · cited by 2,925
- BooleanAlgebrastatement and proof · cited by 300
- inf_le_rightproof · cited by 238
- inf_commproof · cited by 139
- Order.Idealstatement and proof · cited by 102
- Order.Ideal.IsProperstatement and proof · cited by 23
- Order.Ideal.lowerproof · cited by 11
- Order.Ideal.IsPrimestatement · cited by 11
- Order.Ideal.sup_memproof · cited by 5
- sup_inf_inf_complproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Order.Ideal.isPrime_iff_mem_or_compl_memproof · cited by 0